1. The problem statement, all variables and given/known data Hi guys, I was working on this problem and I want to know if it can be solved by using an indefinite integral, so here it goes: A car starts from rest and travels along a straight track such that it accelerates at 10 m/s^2 for 10 s, and then decelerates at 2 m/s^2 . Determine the velocity of the car. 2. Relevant equations My question is if I can solve this using INDEFINITE INTEGRALS ONLY? 3. The attempt at a solution I have obtained the correct answer using a definite integral: For 0 less than or equal to t less than or equal to 10: Integral from 0 to v (1) (dv) = integral from 0 to t (10) dt v=10t For 10 less than or equal to t less than or equal to t' Integral from 100 to v (1) dv = integral from 10 to t (-2 ) dt = v=-2t+120 I'm able to obtain the same result (when using an indefinite integral) for t between 0-10 but for 10-t I cant, also in my book it says that v1 = delta v + v0, well I can clearly see that when using the definite integral but not when I have to use the indefinite integral.. I tried this for t between 10-t : int (1) dv = int (-2) dt = v+c = -2t+C = v=-2t which is incorrect, then I said ok I forgot to add v0 but still I get v=-2t+100 which is still incorrect.. Also if I see it like this: v1= -2t + C + v0 I still cant get a clear understanding because I cant get a value for C.. Please help me and thanks!